Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 20 (2025), 389 -- 402

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ON THE BAUM-CONNES CONJECTURE FOR D∞

Eugenia Ellis, Emanuel Rodríguez Cirone and Gisela Tartaglia

Abstract. One of the most significant contributions to the proof of the Baum-Connes conjecture was made by Higson and Kasparov. Their proof of the conjecture for a-T-menable groups is a highly technical achievement. Some details of this result were later exposed in a survey by Guentner and Higson, where the conjecture for ℤn is approached as an intermediate step to the general case. In this work we review the arguments given for ℤn in the aforementioned survey and show that they apply to the case of the infinite dihedral group.

2020 Mathematics Subject Classification: 46L80, 19K35
Keywords: Operator K-theory, Baum-Connes Conjecture, Equivariant E-theory

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Eugenia Ellis
IMERL, Fac. de Ingeniería, Universidad de la República, Montevideo, Uruguay.
email: eellis@fing.edu.uy

Emanuel Rodríguez Cirone
Área de Matemática - CBC - UBA, Buenos Aires, Argentina.
e-mail:erodriguezcirone@cbc.uba.ar

Gisela Tartaglia - Corresponding author
CMaLP - CONICET, FCE-UNLP, La Plata, Argentina.
e-mail: gtartaglia@mate.unlp.edu.ar

https://www.utgjiu.ro/math/sma